SSPace and Nairu

[dlccmn]

Dear Trubador, dear all
I had problems in estimating with kalman filter the NAIRU.
Here you can find my specification
My Phillips curve is the following

D(core) = C(1) + C(2)*D(core(-2)) + C(3)*(gap) + C(4)*D(gap(-1))

D=first difference,
Core=core inflation (y/y)
Gap=un_rate-Nairu

Un_rate=unemployment rate
Nairu =non accelerating inflation rate of unemployment

The state space specification I used is the following

@signal dcore= c(1)+c(2)*dcore(-2)+c(3)*(un_rate-nairu)+c(4)*(un_rate(-1)-nairu1-un_rate(-2)+nairu2)+[var=exp(c(5))]

@state nairu=nairu(-1)+[var=exp(c(6))]
@state nairu1=nairu(-1)
@state nairu2=nairu1(-1)

I also used starting values and I also initialized state vector
I got an error message, and I really do not understand how I can solve the problem

The starting values come from an LS regression using for the Nairu the OECD estimate.

Please, could you tell me if my specification is correct and where I am wrong?

Thanks in advance for your help
Clemente

I attached my workfile (Eviews 7)

[trubador]

You do not seem to make any errors related to specification of your model in EViews. I think you should first try to increase your sample size, since the current estimation period is limited to 1997Q4-2010Q4 due to lack of observations in your dependent variable (i.e. dcore). Second, you should try to provide additional information on nairu into your model. Although you are aware of the fact that nairu should be extracted from the unemployment variable itself, you did not take this into account in your current specification. I think, something like the following might be more explanatory and structurally more correct:

Code: Select all

@signal dcore= c(1)+c(2)*dcore(-2)+c(3)*u_gap+c(4)*(u_gap1-u_gap2)+[var=exp(c(5))] @signal un_rate = nairu + u_gap @state nairu=2*nairu(-1)-nairu1(-1) + [var=exp(c(6))] @state nairu1=nairu(-1) @state u_gap=[var=exp(c(7))] @state u_gap1=u_gap(-1) @state u_gap2=u_gap1(-1)

Of course you have to adjust your original model accordingly (i.e. initializing state vectors, providing new starting values, etc.)
Finally, I have doubts about the transformation of your dependent variable. I am not sure, but seasonally adjusted quarter-on-quarter inflation might be a better choice than year-on-year specification.

I believe, at this point, any comments from Startz and/or Glenn will provide you with invaluable insights...

[dlccmn]

Dear Trubador, dear all

Many thanks for your comments

You are right, economically UN was not well related to Nairu

Starting from what you suggested, the Phillps curve is

Dcore= c(1)+c(2)*Dcore(-2)+c(3)*un_gap+c(4)*d(un_gap(-1))+er
UN=NAIRU+GAP
As
D=first difference
Core=core inflation (y/y)
Un_gap=UN_rate-NAIRU
UN_rate=unemployment rate
NAIRU non accelerating inflation rate of Unemployment.

I Assume the Nairu follows a random walk with drift while the cyclical component (UN_GAP) is AR(2)

I specified the SSPACE as

@signal dcore= c(1)+c(2)*dcore(-2)+c(3)*u_gap+c(4)*(u_gap1-u_gap3)+[var=exp(c(5))]
@signal un_rate = nairu + u_gap


@state u_gap= c(6)*u_gap(-1) + c(7)*u_gap2(-1) + [var = exp(c(8))]
@state u_gap1=u_gap(-1)
@state u_gap3=u_gap1(-1)
@state u_gap2 = u_gap(-1)
@state nairu=c(9)+nairu(-1)+[var = exp(c(10))]

Results are not encouraging. However, what I would like to know, is if problems are related to a wrong specification of the SSPACE or if have to work on initial condionts and parameter.

Quite often I got a warning message, telling me…
WARNING: Singular covariance - coefficients are not unique

Is this error related to the mis-specification?



Thanks in advance for your help
Clemente De Lucia

[trubador]

State variables ugap1 and ugap2 are both referring to ugap(-1), which makes one of them redundant. Moreover, I think you should still provide more information on nairu, if you still want to estimate it as a random walk. Otherwise, AR(1) specification might be helpful. Please adjust your sample period to 1997Q4-2010Q4 in the estimation dialog box, since your dependent variable has no observations outside this period. The following specification (after supplying better starting values, of course) might be more plausible:

Code: Select all

@signal dcore= c(1)+c(2)*dcore(-2)+c(3)*u_gap+c(4)*(u_gap1-u_gap2)+[var=exp(c(5))] @signal un_rate = nairu + u_gap @state u_gap= c(6)*u_gap(-1) + c(7)*u_gap2(-1) + [var = exp(c(8))] @state u_gap1=u_gap(-1) @state u_gap2=u_gap1(-1) @state nairu=c(9)+c(10)*nairu(-1)+[var = exp(c(11))] param c(1) .0 c(2) .0 c(3) .0 c(4) .0 c(5) .0 c(6) .0 c(7) .0 c(8) .0 c(9) .0 c(10) .0 c(11) .0

However, I still think that your sample size is not enough relative to the number of parameters to be estimated (53 to 11). Other than that, the system you are trying to model is quite flexible and therefore you should provide more observations and/or structural relationships to help identify the latent variables. If you cannot extend the sample size or define additional relationships, then you should carefully provide good initializations for the state variables. And finally, if none of the above works, then it simply means that the system does not behave according to your specifications and that the model is ill-defined.

[powsuarez]

Hello,
I am trying to estimate the NAIRU by using the Phillips curve approach. I am a Bachelor Student so nothing fancy is expected from me.
I tried to regress inflation on unemployment and the constant to get the unemployment coefficient (once i get that coefficient everything is easy...) but the data was too dispersed. I used 3 dummies and LS method...but still my unemployment coefficient comes out something near -0,003 ... I am gonna upload the eviews file with the dummies and i would be SO greatful if somebody could tell me what to do to get a nice unemployment coefficient around 0,42 (i know this from a book). Do i have to change the regression-method? I am backflipping on my chair...this paper is due in 3 days and i cannot get pass this problem!
really appreciate if somebody could help me. THANK YOU.

[startz]

There are two issues:

(1) You should have an inflationary expectations adjusted Phillips curve. Sometimes this means looking at the first difference of inflation.

(2) The results you are getting are standard for a simple econometric estimate. You're not likely to get a textbook estimate.

[powsuarez]

I am using the expectations augmented Phillips Curve, so thats ok. I am using LS...is there anything else I can try? i mean...i am doing it for the SPANISH economy...the series show such a big volatility... i think its gonna be really hard to get something done with the simple LS regression.
No wonder regressing tools then? :-(
What about the SVAR approach? It sounds quite difficult to me to be honest. Any chance I can pull that one off?
thanks, you safe my life!

[startz]

In the workfile you posted, the LHS variable is INF. If that's inflation, then you don't have an expectations-augmented Phillips curve.

You should also check your units of measurement on inflation and unemployment to be sure you understand the units of the slope coefficient. You may not be so far off as you think.